Question: Solve for $p$, $ -\dfrac{7}{5p + 5} = -\dfrac{4p}{3p + 3} - \dfrac{3}{5p + 5} $
Explanation: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $5p + 5$ $3p + 3$ and $5p + 5$ The common denominator is $15p + 15$ To get $15p + 15$ in the denominator of the first term, multiply it by $\frac{3}{3}$ $ -\dfrac{7}{5p + 5} \times \dfrac{3}{3} = -\dfrac{21}{15p + 15} $ To get $15p + 15$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ -\dfrac{4p}{3p + 3} \times \dfrac{5}{5} = -\dfrac{20p}{15p + 15} $ To get $15p + 15$ in the denominator of the third term, multiply it by $\frac{3}{3}$ $ -\dfrac{3}{5p + 5} \times \dfrac{3}{3} = -\dfrac{9}{15p + 15} $ This give us: $ -\dfrac{21}{15p + 15} = -\dfrac{20p}{15p + 15} - \dfrac{9}{15p + 15} $ If we multiply both sides of the equation by $15p + 15$ , we get: $ -21 = -20p - 9$ $ -21 = -20p - 9$ $ -12 = -20p $ $ p = \dfrac{3}{5}$